So, in your interpretation, the only differences between "thaumaturgy with evocation's methods and speed" and evocation are duration and some minor scope changes?
I wouldn't call that a "minor" scope change. The difference in what evocation can do (direct brute-force stuff only), vs what thaumaturgy can do, is
huge. It's like saying that it's just a minor scope change to replace a flashlight with a laptop computer.
And the only changes for evothaum are "with evocation's methods and speed" i.e. you use it just like you would evocation - set a power, call up shifts based on conviction, etc. I really don't understand how you can interpret it as being just "thaumaturgy with no prep"; in my opinion, the text doesn't support that at all.
As for higher end entities being able to use powerful magic with ease: you may note that, for an example, anything at the Lady+ level is, in the books, simply not statted. For others, keep in mind the benefits of sponsor debt. Out of mental stress boxes? No problem; casting something at Conviction+1 would normally cost 2 stress, which you can soak with a point of sponsor debt. If you're totally beholden to your sponsor anyway - i.e. Sidhe, or just that bonkers for kemmlerites / hellfire - why not?
And for making that "powerful magic with ease", well, that's just a case of those NPCs having -10 worth of refinement, or conviction / discipline at +8, or the like.